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SUMMARY:On a deformation of quantum groups and their tensor categories
DTSTART:20221201T101500
DTEND:20221201T111500
DTSTAMP:20260920T150415Z
UID:2f6b3d074c9695d9102d2064119c9fe2302010a93770d8710f2a400a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Azat M. Gainutdinov (Tours)\nFollowing Drinfeld\, one can thin
 k about Drinfeld-Jimbo’s quantum universal enveloping algebras of a simp
 le Lie algebra $\\mathfrak{g}$ in more geometrical terms: they are twist e
 quivalent to the classical universal enveloping algebras with a non-trivia
 l $\\mathfrak{g}$-invariant coassociator which is defined via monodromies 
 of solutions to the Knizhnik-Zamolodchikov equation on 3 points. In other 
 words\, we deal with the representation category of $\\mathfrak{g}$ equipp
 ed with a non-trivial associator\, called Drinfeld’s associator. I am in
 terested in a similar deformation problem for Lusztig’s small quantum gr
 oups at roots of unity\, and more generally\, in deformations of associato
 rs in tensor categories. As it is often in algebra\, infinitesimal deforma
 tions are controlled by Hochschild type complexes\, called in this case Da
 vydov-Yetter complex. I will show how to use a (relative) homological alge
 bra behind such complexes in a rather explicit study of deformations of te
 nsor categories and tensor functors arising in Hopf algebra theory\, in pa
 rticular for Taft algebras and Lusztig’s small quantum groups for sl(2).
  In the latter case we discover new non-trivial deformations (joint with M
 . Faitg and Ch. Schweigert).\n 
LOCATION:GR A3 32 https://plan.epfl.ch/?room==GR%20A3%2032
STATUS:CONFIRMED
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